Raman Spectra of Chondrocytes in Cartilage: hyperspec s chondro data set

Transcription

1 Raman Spectra of Chondrocytes in Cartilage: hyperspec s chondro data set Claudia Beleites <chemometrie@beleites.de> DIA Raman Spectroscopy Group, University of Trieste/Italy (2 28) Spectroscopy Imaging, IPHT, Jena/Germany (28 216) ÖPV, JKI, Berlin/Germany Chemometric Consulting and Chemometrix GmbH, Wölfersheim/Germany October, 217 Reproducing this vignette The data set and source file of this vignette are available at hyperspec s github page at and Renishaw/chondro.txt (ca. 31 MB). The.Rnw looks for rawdata/chondro.txt, so please save the data file in subdirectory rawdata of your working directory. In order to reproduce the examples by typing in the commands, have a look at the definitions of color palettes used in this document are defined in vignettes.defs. Also, the package hyperspec needs to be loaded first via library (hyperspec). Contents 1 Introduction 2 2 The Data Set 2 3 Data Import 3 4 Preprocessing Aligning the Spatial Grid Spectral Smoothing Baseline Correction Normalization Subtracting the Overall Composition Outlier Removal by Principal Component Analysis (PCA) Hierarchical Cluster Analysis (HCA) 7 6 Plotting a False-Colour Map of Certain Spectral Regions 8 1

2 Figure 1 Microphotograph of the cartilage section. The frame indicates the measurement area (3 2 µm). 7 Saving the data set 9 1 Introduction This vignette describes the chondro data set. It shows a complete data analysis work flow on a Raman map demonstrating frequently needed preprocessing methods baseline correction normalization smoothing / interpolating spectra preprocessing the spatial grid and other basic work techniques plotting spectra plotting false color maps cutting the spectral range, selecting (extracting) or deleting spectra, and aggregating spectra (e.g. calculating cluster mean spectra). The chemometric methods used are Principal Component Analysis (PCA) and Hierarchical Cluster Analysis, showing how to use data analysis procedures provided by R and other packages. 2 The Data Set Raman spectra of a cartilage section were measured on each point of a grid, resulting in a so-called Raman map. Figure 1 shows a microscope picture of the measured area and its surroundings. The measurement parameters were: Excitation wavelength: 633 nm Exposure time: s per spectrum Objective:, NA.8 2

3 Measurement grid: 3 2 µm, 1 µm step size Spectrometer: Renishaw InVia 3 Data Import Renishaw provides a converter to export their proprietary data in a so-called long format ASCII file. Raman maps are exported having four columns, y, x, raman shift, and intensity. hyperspec comes with a function to import such files, read.txt.renishaw. The function assumes a map as default, but can also handle single spectra (data = "spc"), time series (data = "ts"), and depth profiles (data = "depth"). In addition, large files may be processed in chunks. In order to speed up the reading read.txt.renishaw does not allow missing values, but it does work with NA. > chondro <- read.txt.renishaw ("rawdata/chondro.txt", data = "xyspc") > chondro hyperspec object 87 spectra 4 data columns 1272 data points / spectrum wavelength: Delta * tilde(nu)/cm^-1 [numeric] data: (87 rows x 4 columns) 1. y: y/(mu * m) [numeric] x: x/(mu * m) [numeric] spc: I / a.u. [matrix1272] NA 4. filename: filename [character] rawdata/chondro.txt rawdata/chondro.txt... rawdata/chondro.txt To get an overview of the spectra (figure 2a): > plot (chondro, "spcprctl") A mean intensity map (figure 2b) is produced by: > plotmap (chondro, func.args = list (na.rm = TRUE), col.regions = seq.palette (2)) plotmap applies a function to squeeze all spectral intensities into a summary characteristic for the whole spectrum. This function defaults to the mean. Further arguments that should be handed to this function can be given in list func.args. As the raw data contains NAs due to deleting cosmic ray spikes, this argument is needed here. I / a.u. y µm ν ~ cm 1 (a) The raw spectra: median, 16 th and 84 th, and th and 9 th percentile spectra. 1 2 x µm (b) The sum intensity of the raw spectra. Figure 2 The raw spectra. 3

4 y y y 4 Preprocessing As usual in Raman spectroscopy of biological tissues, the spectra need some preprocessing. 4.1 Aligning the Spatial Grid The spectra were acquired on a regular square grid of measurement positions over the sample. hyperspec however does not store the data on this grid but rather stores the position where the spectra were taken. This allows more handling of irregular point patterns, and of sparse measurements where not a complete (square) is retained but only few positions on this grid. Occasionally, numeric or rounding errors will lead to seemingly irregular spacing of the data points. This is most obvious in false-colour maps of the sample (fig. fig:raw:b), as plotmap by default uses panel.levelplot.raster which assumes a regular grid is underlying the data. The symptoms are warnings x values are not equispaced; output may be wrong and white stripes in the false colour map (fig 3a) which occur even thought the points are almost at their correct place (fig 3b) > ## disturb a few points > chondro$x [] <- chondro$x [] + rnorm (1, sd =.1) > chondro$y [66] <- chondro$y [66] + rnorm (1, sd =.1) > plotmap (chondro, col.regions = seq.palette (2)) > require ("latticeextra") > plotmap (chondro, col.regions = seq.palette (2), panel = panel.levelplot.points, + col = NA, pch = 22, cex = 1.9) Such slight rounding errors can be corrected by fitraster or makeraster. fitraster needs the step size of the raster and a starting coordinate, whereas makeraster tries to guess these parameters for fitraster. As long as just a few points are affected by rounding errors, makeraster works fine: > chondro$x <- fitraster (chondro$x)$x > chondro$y <- fitraster (chondro$y)$x the result is shown in figure 3c. > plotmap (chondro, col.regions = seq.palette (2)) x (a) Off-grid points cause stripes 1 2 x (b) Slightly wrong coordinages 2 x (c) Corrected grid Figure 3 Rounding erros in the point coordinates of lateral measurement grid. 4.2 Spectral Smoothing As the overview shows that the spectra contain NAs (from cosmic spike removal that was done previously), the first step is to remove these. Also, the wavelength axis of the raw spectra is not 4

5 evenly spaced (the data points are between.8 and 1 cm 1 apart from each other). Furthermore, it would be good to trade some spectral resolution for higher signal to noise ratio. All three of these issues are tackled by interpolating and smoothing of the wavelength axis by spc.loess. The resolution is to be reduced to 8 cm 1, or 4 cm 1 data point spacing. > chondro <- spc.loess (chondro, seq (62, 18, 4)) > chondro hyperspec object 87 spectra 4 data columns 3 data points / spectrum wavelength: Delta * tilde(nu)/cm^-1 [numeric] data: (87 rows x 4 columns) 1. y: y [numeric] x: x [numeric] spc: I / a.u. [matrix3] filename: filename [character] rawdata/chondro.txt rawdata/chondro.txt... rawdata/chondro.txt The spectra are now the same as in the data set chondro. However, the data set also contains the clustering results (see at the very end of this document). They are stored for saving as the distributed demo data: > spectra.to.save <- chondro 4.3 Baseline Correction The next step is a linear baseline correction. spc.fit.poly.below tries to automatically find appropriate support points for polynomial baselines. The default is a linear baseline, which is appropriate in our case: > baselines <- spc.fit.poly.below (chondro) > chondro <- chondro - baselines I / a.u I / a.u ν ~ cm 1 (a) The spectra after smoothing, baseline correction, and normalization ν ~ cm 1 (b) The spectra after subtracting the th percentile spectrum. Figure 4 The preprocessed spectra. 4.4 Normalization As the spectra are quite similar, area normalization should work well:. > chondro <- chondro / rowmeans (chondro) > plot (chondro, "spcprctl")

6 Note that normalization effectively cancels the information of one variate (wavelength), it introduces a collinearity. If needed, this collinearity can be broken by removing one of the variates involved in the normalization. Note that the chondro object shipped with hyperspec set has multiple collinearities as only the first principal components are shipped (see below). For the results of these preprocessing steps, see figure 4a. 4. Subtracting the Overall Composition The spectra are very homogeneous, but I m interested in the differences between the different regions of the sample. Subtracting the minimum spectrum cancels out the matrix composition that is common to all spectra. But the minimum spectrum also picks up a lot of noise. So instead, the th percentile spectrum is subtracted: > chondro <- chondro - quantile (chondro,.) > plot (chondro, "spcprctl") The resulting data set is shown in figure 4b. Some interesting differences start to show up: there are distinct lipid bands in some but not all of the spectra. 4.6 Outlier Removal by Principal Component Analysis (PCA) PCA is a technique that decomposes the data into scores and loadings (virtual spectra). It is known to be quite sensitive to outliers. Thus, I use it for outlier detection. The resulting scores and loadings are put again into hyperspec objects by decomposition: > pca <- prcomp (chondro, center = TRUE) > scores <- decomposition (chondro, pca$x, label.wavelength = "PC", + label.spc = "score / a.u.") > loadings <- decomposition (chondro, t(pca$rotation), scores = FALSE, + label.spc = "loading I / a.u.") Plotting the scores of each PC against all other gives a good idea where to look for outliers. > pairs (scores [[,,1:2]], pch = 19, cex =.) Now the spectra can be found either by plotting two scores against each other (by plot) and identifying with identify, or they can be identified in the score map by map.identify. There is also a function to identify spectra in a spectra plot, spc.identify, which could be used to identify principal components that are heavily influenced e. g. by cosmic ray spikes. > ## omit the first 4 PCs > out <- map.identify (scores [,,]) > out <- c (out, map.identify (scores [,,6])) > out <- c (out, map.identify (scores [,,7])) > out [1] > outcols <- c ("red", "blue", "#88", "orange", "magenta", "brown") > cols <- rep ("black", nrow(chondro)) > cols [out] <- outcols We can check our findings by comparing the spectra to the bulk of spectra (figure a): 6

7 > plot(chondro[1], plot.args = list (ylim = c (1, length (out) +.7)), + lines.args = list( type = "n")) > for (i in seq (along = out)){ + plot(chondro, "spcprctl", yoffset = i, add = TRUE, col = "gray") + plot (chondro [out[i]], yoffset = i, col = outcols[i], add = TRUE, + lines.args = list (lwd = 2)) + text (6, i +.33, out [i]) + } and also by looking where these spectra appear in the scores pairs plot (figure b): > png ("chondro-fig--pca-pairs2.png", width =, height = ) > pch <- rep (46L, nrow (chondro)) > pch [out] <- 19L > pairs (scores [[,,1:7]], pch = pch, cex = 1, col = cols) > dev.off () Finally, the outliers are removed: > chondro <- chondro [- out] 69 I / a.u ν ~ cm 1 (a) The suspected outlier spectra. (b) pairs plot of the first 7 scores. Hierarchical Cluster Analysis (HCA) HCA merges objects according to their (dis)similarity into clusters. The result is a dendrogram, a graph stating at which level two objects are similar and thus grouped together. The first step in HCA is the choice of the distance. The R function dist offers a variety of distance measures to be computed. The so-called Pearson distance D 2 Pear son = 1 COR(X ) 2 is popular in data analysis of vibrational spectra and is provided by hyperspec s pearson.dist function. Also for computing the dendrogram, a number of choices are available. Here we choose Ward s method, and, as it uses Euclidean distance for calculating the dendrogram, Euclidean distance also for the distance matrix : 7

8 > dist <- dist (chondro) > dendrogram <- hclust (dist, method = "ward.d") > plot (dendrogram) In order to get clusters, the dendrogram is cut at a level specified either by height or by the number of clusters. > chondro$clusters <- as.factor (cutree (dendrogram, k = 3)) > cols <- c ("dark blue", "orange", "#C22") The result for k= 3 clusters is plotted as a map (figure b). If the color-coded variate (left hand side of the formula) is a factor, the legend bar does not show intermediate colors, and hyperspec s levelplot method uses the levels of the factor for the legend. Thus meaningful names are assigned > levels (chondro$clusters) <- c ("matrix", "lacuna", "cell") and the cluster membership map is plotted: > print (plotmap (chondro, clusters ~ x * y, col.regions = cols)) The cluster membership can also be marked in the dendrogram: > par (xpd = TRUE) # allow plotting the markers into the margin > plot (dendrogram, labels = FALSE, hang = -1) > mark.dendrogram (dendrogram, chondro$clusters, col = cols) Figure a shows the dendrogram and b the resulting cluster map. The three clusters correspond to the cartilage matrix, the lacuna and the cells. The left cell is destroyed and its contents are leaking into the matrix, while the right cells looks intact. We can plot the cluster mean spectra ± 1 standard deviation using aggregate (see figure 6): > cluster.means <- aggregate (chondro, chondro$clusters, mean_pm_sd) > plot (cluster.means, stacked = ".aggregate", fill = ".aggregate", col = cols) Height Cluster Dendrogram y 1 cell lacuna matrix matrix cell lacuna (a) dist The dendrogram. Figure 2 x (b) The cluster map for k = 3 clusters. Hierarchical cluster analysis. 6 Plotting a False-Colour Map of Certain Spectral Regions hyperspec comes with a sophisticated interface for specifying spectral ranges. Expressing things like cm -1 ± 1 data points is easily possible. Thus, we can have a fast look at the nucleic acid distribution, using the DNA bands at 728, 782, 98, 124, 1482, and 177 cm -1 : 8

9 I / a.u. matrix lacuna cell ν ~ cm 1 Figure 6 The cluster mean ± 1 standard deviation spectra. The blue cluster shows distinct lipid bands, the yellow cluster collagen, and the red cluster proteins and nucleic acids. > plotmap (chondro[,, c( 728, 782, 98, 124, 1482, 177)], + col.regions = colorramppalette (c("white", "gold", "dark green"), space = "Lab") (2)) y.. 2 x Figure 7 False colour map of the DNA band intensities. The result is shown in figure 7. While the nucleus of the right cell shows up nicely, nothing is detected in the remainders of the left cell. 7 Saving the data set Finally, the example data set is put together and saved. In order to keep the package size small, only a PCA-compressed version with PCs is shipped as example data set of the package. > spectra.to.save$clusters <- factor (NA, levels = levels (chondro$clusters)) > spectra.to.save$clusters[- out] <- chondro$clusters > pca <- prcomp (spectra.to.save) >.chondro.scores <- pca$x [, seq_len ()] >.chondro.loadings <- pca$rot [, seq_len ()] >.chondro.center <- pca$center >.chondro.wl <- wl (chondro) >.chondro.labels <- lapply (labels (chondro), as.expression) >.chondro.extra <- spectra.to.save$.. > save (.chondro.scores,.chondro.loadings,.chondro.center, 9

10 +.chondro.wl,.chondro.labels,.chondro.extra, + file = "chondro-internal.rda") This is the file distributed with hyperspec as example data set. Session Info R version ( ) Platform: x86_64-pc-linux-gnu (64-bit) Running under: Ubuntu LTS Matrix products: default BLAS/LAPACK: /usr/lib/openblas/lib/libopenblas_haswellp-r.2.19.so locale: [1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C LC_TIME=de_DE.UTF-8 [4] LC_COLLATE=de_DE.UTF-8 LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8 [7] LC_PAPER=de_DE.UTF-8 LC_NAME=C LC_ADDRESS=C [] LC_TELEPHONE=C LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C attached base packages: [1] grid stats graphics grdevices utils datasets methods base other attached packages: [1] latticeextra_.6-28 RColorBrewer_1.1-2 hyperspec_ ggplot2_2.2.1 [] lattice_.2-3 loaded via a namespace (and not attached): [1] Rcpp_ crayon_1.3.4 plyr_1.8.4 R6_2.2.2 gtable_.2. [6] magrittr_1. scales_.. rlang_.1.2 lazyeval_.2. rstudioapi_.7 [11] testthat_1..2 tools_3.4.2 munsell_.4.3 compiler_3.4.2 colorspace_1.3-2 [16] tibble_1.3.4